I believe you mean compare to kJ/mol right? and heat of combustion?
Well kJ/mol is measured by one mole of a substance. For example 1 mol of methanol = about 32 g, ethanol is about 46 g etc. However this isn't a fair comparison in the sense that one mole of a substance is dependent on its MM.
kJ/g is the better measure since you have 1 g of each substance. Comparing one gram of ethanol to one gram of 1-propanol gives a fair test between the two alkanols.
To put it into perspective, say if you have 2 trees, each with varying height. You take one mole of each tree and burn it, you would get different amounts of heat of combustion since one mole of the largest tree is much greater than the little tree. However, if you take one gram of each tree, then you have one gram of tree to test as a comparison. Therefore its a fair test.
Hope that explains a bit?